Linear quadratic mean field social control with common noise: A directly decoupling method?

doi:10.1016/j.automatica.2022.110619

	Linear quadratic mean field social control with common noise: A directly decoupling method?
	Wang, Bing-Chang 1; Zhang, Huanshui 2; Zhang, Ji-Feng 3,4
刊名	AUTOMATICA
	2022-12-01
卷号	146 页码:14
关键词	Mean field game Optimal social cost Stabilization Finite agents Common noise FBSDE
ISSN号	0005-1098
DOI	10.1016/j.automatica.2022.110619
英文摘要	This paper is concerned with mean field linear quadratic social control with common noise, where the weight matrices of individual costs are indefinite We first obtain a set of forward-backward stochastic differential equations (FBSDEs) from variational analysis, and then construct a centralized feedback representation by decoupling the FBSDEs. By using solutions of two Riccati equations, we design a set of decentralized control laws, which is further shown to be asymptotically social optimal. The necessary and sufficient conditions are given for uniform stabilization of the systems by exploiting the relation between population state average and aggregate effect. An explicit expression of the optimal social cost is given in terms of two Riccati equations. Besides, the decentralized optimal solution is provided for mean field social control problem with finite agents.
资助项目	National Key R&D Program of China[2018YFA0703800] ; National Natural Science Foundation of China[61877057] ; National Natural Science Foundation of China[61922051] ; National Natural Science Foundation of China[62122043] ; National Natural Science Foundation of China[62192753] ; Major Basic Research of Natural Science Foundation of Shandong Province, China[ZR2021ZD14] ; Major Basic Research of Natural Science Foundation of Shandong Province, China[ZR2020ZD24] ; Science and Technology Project of Qingdao West Coast New Area, China[2019-32] ; Science and Technology Project of Qingdao West Coast New Area, China[2020-20] ; Science and Technology Project of Qingdao West Coast New Area, China[2020-1-4] ; High-level Talent Team Project of Qingdao West Coast New Area, China[RCTDJC-2019-05] ; Key Research and Development Program of Shandong Province, China[2020CXGC01208]
WOS研究方向	Automation & Control Systems ; Engineering
语种	英语
出版者	PERGAMON-ELSEVIER SCIENCE LTD
WOS记录号	WOS:000870698100001
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/60785]
专题	中国科学院数学与系统科学研究院
通讯作者	Zhang, Ji-Feng
作者单位	1.Shandong Univ, Sch Control Sci & Engn, Jinan 250061, Peoples R China 2.Shandong Univ Sci & Technol, Coll Elect Engn & Automation, Qingdao 266590, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China 4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100149, Peoples R China
推荐引用方式 GB/T 7714	Wang, Bing-Chang,Zhang, Huanshui,Zhang, Ji-Feng. Linear quadratic mean field social control with common noise: A directly decoupling method?[J]. AUTOMATICA,2022,146:14.
APA	Wang, Bing-Chang,Zhang, Huanshui,&Zhang, Ji-Feng.(2022).Linear quadratic mean field social control with common noise: A directly decoupling method?.AUTOMATICA,146,14.
MLA	Wang, Bing-Chang,et al."Linear quadratic mean field social control with common noise: A directly decoupling method?".AUTOMATICA 146(2022):14.